Effect Of Power-law Exponent Research Articles

Fluid–structure interaction in engineering based on its applications: A plenary and up-to-date review

The present study reviews the relevant research done on the fluid–structure interaction (FSI) in channels and vessels. The cases of FSI in channels with elastic plates, channels with variable geometry, flow airfoils, blood vessels, and heart valves are presented, using data from credible research articles. The review is carried out with a focus on the performance of the FSI method in solving engineering problems in channels, reporting its findings such as the effect of power-law exponent, the Nusselt number in different parts of a fluid, lift, and drag for a rigid cylinder and a plate in Newtonian fluids, the formation of eddy current, and the distribution of velocity and pressure in a fluid and on walls. The review is instrumental for researchers, engineers, and academics in providing comprehensive insight into methodologies and applications of fluid–structure interaction.

Nonlinear Free Vibration of Spinning Pre-Twisted Functionally Graded Material Plates in Thermal Environment

This paper investigates the nonlinear free vibration of spinning pre-twisted functionally graded material (FGM) plates in thermal environment. Based on the Kirchhoff plate theory and von Kármán large-deformation theory, the nonlinear dynamic model is established via the Lagrange equation, where the warping effect is taken into account. The material properties are related to temperature and change according to a power-law exponent distribution. The theoretical solution of nonlinear-free vibration is obtained using the multiple scale method. The effects of power-law exponent, temperature difference, spinning speed, hub radius ratio, and twist angle on nonlinear-free vibration characteristics of the spinning pre-twisted cantilever FGM plates are discussed. The results show that the spinning pre-twisted cantilever FGM plate exhibits nonlinear hardening-spring vibration behavior, while the characteristics weaken with the increase of spinning speed. The twist angle and setting angle have coupling effects on the nonlinear vibration characteristics of spinning pre-twisted FGM plates.

Application of Haar wavelet discretization and differential quadrature methods for free vibration of functionally graded micro-beam with porosity using modified couple stress theory

The present investigation is aimed at the implementation of Haar Wavelet Discretization Method (HWDM) and Differential Quadrature Method (DQM) on the free vibration of a Functionally Graded (FG) micro-beam with uniformly distributed porosity along the thickness. As per the power-law exponent model, the material properties such as Young's modulus, and mass density are varied along the thickness of the FG micro-beam and the beam is made up of Aluminum (Al) as metal constituent and Alumina (Al2O3) as ceramic constituent. Modified couple stress theory is employed to capture the small scale effect and pointwise convergence studies for HWDM as well as DQM have also been carried out to exhibit the effectiveness of the methods with respect to the undertaken problem. The results obtained by both methods are compared to demonstrate the accuracy of the present model, revealing excellent accuracy. The effect of power-law exponent, porosity volume fraction index, and thickness to material length scale parameter on the natural frequencies is thoroughly investigated with proper physical explanations for Hinged-Hinged (H-H), Clamped-Hinged (C-H), Clamped-Clamped (C-C), and Clamped-Free (C-F) boundary conditions. Further, mode shapes are also plotted for qualitatively assessing the dynamics of the structural component.

Nonlocal strain gradient theory for dynamical modeling of a thermo-piezo-magnetically actuated spinning inhomogeneous nanoshell

As the main contribution, a nonlocal strain gradient theory (NSGT) is developed in conjugation with the generalized differential quadrature method (GDQM) to analyze the free vibration of a transversely graded nanoshell subjected to magnetic and thermal loads derived by using the first-order shear deformation theory (FSDT) and Hamilton’s principle. Comparisons with other common methods have shown the validity of the presented NSGT-GDQM hybrid approach. The effects of power-law exponent, nonlocal parameter, strain gradient parameter, magnetic potential, angular velocity, and temperature for both simply supported and clamped boundary conditions of a nanoshell composed of BaTiO3 and CoFe2O4 materials were investigated. Sensitivity analysis illustrates that more resolution will be available with clamped boundaries. With increasing the temperature gradient, the absolute value of the sensitivity increases and the maximum sensitivity value occurs always on the critical buckling point. Finally, comparing two studied boundary conditions revealed that if there is any temperature rise limit, the clamped boundary condition is suggested because of more sensitivity. Though the temperature gradient could be more than 400 K in the case of simply supported edges, the maximum absolute sensitivity could be obtained is about 0.12 wherein the case of clamped boundary condition it was about 0.17.

Application of shifted Chebyshev polynomial-based Rayleigh–Ritz method and Navier’s technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation

The present study is dealt with the applicability of shifted Chebyshev polynomial-based Rayleigh–Ritz method and Navier’s technique on free vibration of functionally graded (FG) beam with uniformly distributed porosity along the thickness of the beam. The material properties such as Young’s modulus, mass density, and Poisson’s ratio are also considered to vary along the thickness of the FG beam as per the power-law exponent model. The porous FG beam is embedded in an elastic substrate; namely, the Kerr elastic foundation and the displacement field of the beam are governed by a refined higher-order shear deformation theory. The effectiveness of the Rayleigh–Ritz method is due to the use of the shifted Chebyshev polynomials as a shape function. The orthogonality of shifted Chebyshev polynomial makes the technique more computationally efficient and avoid ill-conditioning for the higher number of terms of the polynomial. Hinged–hinged, clamped–hinged, clamped–clamped, and clamped-free boundary conditions have been taken into account for the parametric study. Validation of the present model is examined by comparing it with the existing literature in special cases showing remarkable agreement. A pointwise convergence study is also carried out for shifted Chebyshev polynomial-based Rayleigh–Ritz method, and the effect of power-law exponent, porosity volume fraction index, and elastic foundation on natural frequencies is studied comprehensively.

Free vibration and buckling analyses of functionally graded annular thin sector plate in-plane loads using GDQM

In the present study, buckling and free vibration analyses of annular thin sector plate made of functionally graded materials (FGMs) resting on visco-elastic Pasternak foundation, subjected to external radial, circumferential and shear in-plane loads is investigated. Material properties are assumed to vary along the thickness according to an power law with Poisson\'s ratio held constant. First, based on the classical plate theory (CPT), the governing equation of motion is derived using Hamilton\'s principle and then is solved using the generalized differential quadrature method (GDQM). Numerical results are compared to those available in the literature to validate the convergence and accuracy of the present approach. Finally, the effects of power-law exponent, ratio of radii, thickness of the plate, sector angle, and coefficients of foundation on the fundamental and higher natural frequencies of transverse vibration and critical buckling loads are considered for various boundary conditions. Also, vibration and buckling mode shapes of functionally graded (FG) sector plate have been shown in this research. One of the important obtained results from this work show that ratio of the frequency of FG annular sector plate to the corresponding values of homogeneous plate are independent from boundary conditions and frequency number.

Application of two-steps perturbation technique to geometrically nonlinear analysis of long FGM cylindrical panels on elastic foundation under thermal load

ABSTRACTPresent research deals with the geometrically nonlinear bending of a long cylindrical panel made of a through-the-thickness functionally graded material subjected to thermal load. A panel under the action of uniform temperature rise loading is considered. Formulation of the shell is based on the third-order shear deformation shell theory, where the first-order shear deformation and classical shell theory may be extracted as special cases. Thermomechanical properties of the shell are assumed to be temperature dependent and are estimated according to a power law function across the shell thickness. Also, it is assumed that shell is in contact with an elastic foundation which acts in tension as well as in compression. The nonlinear governing equations of the shell are obtained using the von Kármán type of geometrical nonlinearity. The obtained governing equations are solved for two cases, i.e., simply supported shells and clamped shells. The developed equations are solved using a two-step perturbation technique. Accurate closed-form expressions are provided to obtain the mid-span deflection of the shell as a function of temperature elevation. Numerical results are provided to analyze the effects of power law exponent, boundary conditions, temperature dependency, side to radius ratio, and side to thickness ratio.

Exact solution for in-plane static problems of circular beams made of functionally graded materials

ABSTRACTExact analytical solutions of in-plane static problems of circular beams with uniform cross-section made of functionally graded material (FGM) are obtained. Material properties are assumed to be varying arbitrarily through the thickness. The effects of axial extension and shear deformations are considered. The differential equation system is solved exactly using the initial values method. The circumferential stress distribution on the cross-section is also obtained. The results are compared with those of rather complex approaches in the literature, such as elasticity approach, and the comparison shows an excellent agreement. Effects of power law exponent and radius-to-height ratio of the beam on circumferential stress distribution and displacements are investigated.

Nonlinear forced vibration of functionally graded cylindrical thin shells

The nonlinear forced vibration of infinitely long functionally graded cylindrical shells is studied using the Lagrangian theory and multiple scale method. The equivalent properties of functionally graded materials are described as a power-law distribution in the thickness direction. The energy approach is applied to derive the reduced low-dimensional nonlinear ordinary differential equations of motion. Using the multiple scale method, a special case is investigated when there is a 1:2 internal resonance between two modes and the excitation frequency is close to the higher natural frequency. The amplitude–frequency curves and the bifurcation behavior of the system are analyzed using numerical continuation method, and the path leading the system to chaos is revealed. The evolution of symmetry is depicted by both the perturbation method and the numerical Poincaré maps. The effect of power-law exponent on the amplitude response of the system is also discussed.

MHD micropumping of power-law fluids: A numerical solution

The performance of MHD micropumps is studied numerically assuming that the viscosity of the fluid is shear-dependent. Using power-law model to represent the fluid of interest, the effect of power-law exponent, N, is investigated on the volumetric flow rate in a rectangular channel. Assuming that the flow is laminar, incompressible, two-dimensional, but (approximately) unidirectional, finite difference method (FDM) is used to solve the governing equations. It is found that shear-thinning fluids provide a larger flow rate as compared to Newtonian fluids provided that the Hartmann number is above a critical value. There exists also an optimum Hartmann number (which is larger than the critical Hartmann number) at which the flow rate is maximum. The power-law exponent, N, strongly affects the optimum geometry depending on the Hartmann number being smaller or larger than the critical Hartmann number.

A mixed analytical-numerical investigation of snap-through of low arches with a power-law variable thickness

Snap-through is an instability phenomenon that occurs in arch and dome-shaped structures, wherein the structure has to move from a stable equilibrium state through an unstable path into another stable equilibrated configuration in a jumping action. In this study, a linear elastic isotropic low arch is considered as a structure with power-law variable thickness. The phenomenon is investigated by considering the equation of the deflection for the variable thickness arch, solving it with an elegant analytical technique, and finding the snap-through critical load from an extreme condition. The effect of power-law exponent and geometry of the arch centerline on critical load is investigated and the constant thickness case and a very rare case of power-law thickness variation found in literature are considered for verification.

Mathematical solution for bending of short hybrid composite beams with variable fibers spacing

In this study, the static response is presented for a simply supported functionally graded hybrid beam subjected to a transverse uniform load. Material properties of the beam are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. By varying the fiber volume fraction within a symmetric laminated beam and combining two fiber types to create a hybrid functionally graded material (FGM) can offer desirable increases in axial and bending stiffness. The equations governing the hybrid FGM beams are determined using the principle of virtual work (PVW) arising from the higher order shear deformation theories. Numerical results on the transverse deflection, axial and shear stresses in a moderately thick hybrid FGM beam under uniform distributed load are discussed in depth. The effect of power-law exponent on the deflection and stresses are also commented.

Static analysis of functionally graded beams using higher order shear deformation theory

Displacement field based on higher order shear deformation theory is implemented to study the static behavior of functionally graded metal–ceramic (FGM) beams under ambient temperature. FGM beams with variation of volume fraction of metal or ceramic based on power law exponent are considered. Using the principle of stationary potential energy, the finite element form of static equilibrium equation for FGM beam is presented. Two stiffness matrices are thus derived so that one among them will reflect the influence of rotation of the normal and the other shear rotation. Numerical results on the transverse deflection, axial and shear stresses in a moderately thick FGM beam under uniform distributed load for clamped–clamped and simply supported boundary conditions are discussed in depth. The effect of power law exponent for various combination of metal–ceramic FGM beam on the deflection and stresses are also commented. The studies reveal that, depending on whether the loading is on the ceramic rich face or metal rich face of the beam, the static deflection and the static stresses in the beam do not remain the same.

Dynamic stability of functionally graded plate underin‐plane compression

Functionally graded materials have gained considerable attention in the high‐temperature applications. A study of parametric vibrations of functionally graded plates subjected to in‐plane time‐dependent forces is presented. Moderately large deflection equations taking into account a coupling of in‐plane and transverse motions are used. Material properties are graded in the thickness direction of the plate according to volume fraction power law distribution. An oscillating temperature causes generation of in‐plane time‐dependent forces destabilizing the plane state of the plate equilibrium. The asymptotic stability and almost‐sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov′s direct method. Effects of power law exponent on the stability domains are studied.